Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

Martin Reuter; Frank Saueressig

doi:10.1007/JHEP12(2011)012

paper

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

arXiv:1110.5224 · doi:10.1007/JHEP12(2011)012

Abstract

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_{s}$ and walk dimension $d_{w}$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_{s} = d, d_{w} = 2$ , a semi-classical regime where $d_{s} = 2 d / (2 + d), d_{w} = 2 + d$ , and the UV-fixed point regime where $d_{s} = d /2, d_{w} = 4$ . On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.

26 pages, 6 figures

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

Abstract

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